Evaluating Change in Adjusted R-Square and R-Square Indices: A Latent Variable Method Application.

Abstract

A procedure for interval estimation of the difference in the adjusted R-square index for nested linear models is discussed. The method yields as a byproduct confidence intervals for their standard R-square difference, as well as for the adjusted and standard R-squares associated with each model. The resulting interval estimate of the difference in adjusted R-square represents a useful and informative complement to the commonly used R-square change statistic and its significance test in model selection and contains substantially more information than that test. The outlined procedure is readily employed with popular software in empirical educational and psychological studies and is illustrated with numerical data.